This wrecked me a little at first because I kept wanting to anchor on some number I half-remembered and couldn't.
Break the problem into two independent estimates: total annual Netflix spending in the US and the average price of a US home. Derive each from first principles using a clear, defensible chain of assumptions, then divide to get the number of homes. Sanity-check the final figure against known benchmarks (e.g., Netflix revenue, typical home prices) to ensure plausibility.
Pro tip: State your assumptions explicitly and round aggressively to keep the mental math clean—interviewers care more about your structured reasoning than precise arithmetic. If time allows, briefly mention how you'd validate or refine your estimate with real data.
Start with the US population (~330M), assume an average household size of ~2.5 people, and estimate the fraction of households that subscribe to Netflix (e.g., ~60-70%). Multiply to get the number of subscribing households.
Assume a typical monthly subscription price (e.g., $15) and multiply by 12 to get annual revenue per subscriber. Optionally adjust for plan mix (basic, standard, premium) or account sharing.
Multiply the number of subscribers by the annual revenue per subscriber. This gives the total amount Americans spend on Netflix subscriptions each year.
Use a rough median or average home price (e.g., $300k-$400k) based on general knowledge. Justify the figure by referencing typical housing markets or recent trends.
Divide total annual Netflix spending by the average home price to get the number of homes. Sanity-check by comparing to known figures (e.g., Netflix's total revenue, US housing market size) and discuss potential biases.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Easier once you frame it right: one source of uncertainty just got removed, so the interval should shrink.
Acknowledge the new information as a data point that should be incorporated into your prior estimate using Bayesian updating. Recalculate your point estimate and confidence interval, then explain how the interval width changes based on the precision of the new information relative to your prior. Emphasize that the interval should narrow because you have more information, but the exact amount depends on the reliability of the new data.
Pro tip: Show that you understand the difference between a confidence interval and a credible interval, and that in a Bayesian framework, the posterior interval will be narrower if the new data is precise. Also, mention that if the new information is inconsistent with your prior, you might need to reassess your assumptions.
Briefly summarize your initial estimate and confidence interval for Netflix US subscribers before receiving the new information. This sets the baseline for updating.
Consider the source and reliability of the 'roughly 81 million' figure. Is it from a credible report? How precise is it? This determines how much weight to give it.
Combine your prior with the new data using a weighted average or Bayesian updating. If the new data is very reliable, your updated estimate should be close to 81 million; otherwise, it will be a compromise.
Determine the new interval width. Generally, incorporating additional independent information reduces uncertainty, so the interval should get narrower. The amount depends on the precision of the new data relative to your prior.
Articulate that the interval narrows because you have more information, but if the new data is vague (e.g., 'roughly'), the reduction may be modest. Quantify if possible.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the underlying quantity and your 90% interval, then translate that interval into a bid-ask spread by centering around the median and setting the spread width based on your confidence and risk tolerance. Explain how the interval bounds inform the maximum acceptable loss and thus the width of the market you'd quote.
Pro tip: In market making, your bid-ask spread should reflect both your uncertainty and the need to manage inventory risk; a tighter spread increases fill probability but also adverse selection risk, so balance the two by considering the expected flow.
Restate the quantity being priced and confirm that the 90% interval represents your subjective belief about its true value. Ensure you understand whether the interval is for a future outcome or a current estimate.
Use the midpoint of your 90% interval as the basis for your mid-price. This represents your best estimate of the fair value.
Decide on the bid-ask spread based on your uncertainty (interval width) and desired profit margin. A wider interval suggests greater uncertainty, warranting a wider spread to protect against adverse selection.
Place the bid below the mid and the ask above the mid, ensuring the spread captures your edge. For example, if mid is M and spread is S, bid = M - S/2, ask = M + S/2.
Explain that the interval bounds represent extreme scenarios; your bid should be above the lower bound (to avoid buying too low) and your ask below the upper bound (to avoid selling too high), but the spread should be narrower than the full interval to remain competitive.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify the context of the estimation problem (e.g., market sizing, revenue projection) and list the remaining unknown assumptions. Then, evaluate each unknown based on its impact on the final answer and the uncertainty surrounding it, and select the one that would most reduce overall uncertainty or drive the decision.
Pro tip: Frame your choice in terms of sensitivity and decision impact: the most valuable unknown is often the one that the final metric is most sensitive to and that is currently most uncertain. This shows you think like a data scientist who prioritizes reducing risk.
Restate the problem and the objective of the estimation (e.g., to size a market, forecast revenue). Identify what decision or conclusion the estimate will inform.
Enumerate the assumptions that are still unknown after the subscriber count is given. For example, average revenue per user, churn rate, growth rate, etc.
For each unknown, consider how much it affects the final output (sensitivity) and how uncertain it currently is. A highly sensitive and highly uncertain variable is a prime candidate.
Choose the single unknown that would most reduce overall uncertainty or most influence the decision. Justify your choice by explaining its leverage.
Briefly describe how you might obtain that unknown (e.g., A/B test, survey, historical data) to show practicality.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify that the original answer likely used a national median house price, which is a single aggregate. Then, explain that switching to San Francisco homes introduces a different distribution: much higher median, greater variance, and different drivers (tech industry, limited supply). Finally, discuss how this changes the answer depending on the specific question—e.g., affordability, investment returns, or market predictions—and emphasize the need to adjust models and assumptions accordingly.
Pro tip: Show that you understand the difference between a national median and a local market by mentioning that San Francisco's housing market is not just a scaled-up version of the national one; it has unique dynamics like extreme income inequality and rent control that affect price behavior.
Restate what the original answer was about (e.g., predicting house prices, calculating affordability) and confirm that it used national median price as a baseline.
List factors that make SF housing distinct: higher median price (over $1M), lower inventory, higher demand from tech workers, stricter zoning, and greater price volatility.
Explain how these differences change the answer: e.g., affordability metrics shift dramatically, investment returns may be lower due to high entry cost, and predictive models need local features.
Suggest that the candidate would need to re-run analyses with SF-specific data, consider sub-markets (e.g., neighborhoods), and possibly use different models that account for spatial correlation.
Summarize that the answer becomes more nuanced and localized, and that generalizing from national data to SF can lead to misleading conclusions.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is just a coverage test and I knew it, but I stumbled on the wording.
Explain that you would simulate or collect 100 independent 90% confidence intervals and count how many contain the true parameter. If the coverage is close to 90 (e.g., between 85 and 95), the intervals are well-calibrated; otherwise, investigate potential causes like model misspecification or incorrect standard errors.
Pro tip: Mention that calibration should be checked on held-out data or through simulation, and that you would also examine the width of intervals and coverage across different subgroups to ensure robustness.
Clarify that you need 100 independent samples or simulations where the true parameter is known, and for each, compute a 90% confidence interval.
Count how many of the 100 intervals contain the true parameter value. The expected number is 90 if the intervals are perfectly calibrated.
Compare the observed coverage to 90%. Use a binomial test or confidence interval for the coverage proportion to determine if the difference is statistically significant.
If coverage is off, investigate potential reasons: incorrect standard errors, model assumptions violated, dependence between intervals, or non-normal distributions.
Adjust the method (e.g., use bootstrap, robust standard errors, or Bayesian intervals) and re-evaluate calibration until coverage is acceptable.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.